The need for highly secure radio and wireline communications in smaller products is increasing, due in part to the increased desire to use the communications for business and financial transactions, and due in part to the widespread use of smaller two way radios. A vital factor in attaining highly secure communication is the availability of number generators that are essentially purely random. A variety of electronic circuits exist to generate numbers that are random to varying degrees. Random numbers are commonly generated in the form of a binary signal having a sample clock rate, f.sub.s Hertz (Hz). One characteristic of an ideal random binary signal is a spectral energy density that is uniform from 0 Hz (DC) to f.sub.s /2. Another characteristic of an ideal random binary signal is a lack of deterministic behavior.
There are a variety of circuits that generate clocked binary signals that are within varying degrees of being close to ideal in their measure of randomness. For example, there are circuits based on diode noise that are quite good in this respect. However, they typically suffer from a susceptibility to intentional radio frequency (RF) interference, wherein the RF interference is intentionally deterministic and causes the circuit to become more deterministic, and thus less random. In another example, radioactive decay provides a good source of random values, but the radioactive source is complicated to handle (shield), and the operation of the electronic circuit used to convert the physical effect into an electronic signal, and the operation of other surrounding circuits, can be susceptible to malfunction from the radiation. Other electronic circuits that rely less directly on such fundamental effects generally provide signals that are more deterministic and that exhibit less uniform spectral energy density.
One type of electronic circuit that provides a chaotic signal having some desirable random characteristics is a third order Chua's oscillator, comprising a third order linear circuit coupled to a non-linear diode-like element having a negative slope in the diode transition region. In one configuration of Chua's oscillator, the non-linear diode-like element is implemented using operational amplifiers. Chua's oscillator circuit provides a chaotic signal when the circuit is operating in a chaotic mode, in which the oscillations of the circuit chaotically alter around phase space points called, in chaotic theory, the "attractors" of the circuit. The frequency spectrum of Chua's oscillator circuit is fairly uniformly distributed from DC up to a frequency, termed herein the upper characteristic frequency, that is dependent on the values of the linear elements and the shape of the input-output function of the non-linear element. Chua's oscillator comprises conventional linear devices (e.g., resistors, capacitors, and inductors) to establish the linear parameters, and it is susceptible to production and environmental variations of the values of the linear devices that can cause the oscillator to stop oscillating, or oscillate around only one of the attractors, occurrences that render it essentially useless. Furthermore, the operation of the circuit is deterministic, which makes it non-ideal for use in situations demanding high security.
Attempts have been made to eliminate the problem in Chua's oscillator of the loss of chaotic behavior due to variations of the circuit element values, while also eliminating another problem--the physical size of passive elements (capacitors, inductors). The attempts include an integrated circuit implementation using a circuit topology that is designed using state-variable synthesis. This approach, described in a technical paper by A. Rodriguez-Vasquez and M Delgado-Restituto, entitled "Design Considerations for Integrated Continuous-Time Chaotic Oscillators," IEEE Trans. Circuits Syst. I vol. 45, pp. 481-495, April 1998, makes use of transconductors and capacitors that are more optimal for an integrated circuit implementation. However, it does not eliminate the deterministic characteristics of the chaotic behavior.
Thus, what is needed is a binary random signal that is non-deterministic and has white noise characteristics over a wide frequency range.